# Does the relativity of simultaneity imply a sort of determinism?

1. Feb 28, 2013

### RLutz

This came up at lunch today when a friend of mine brought up that he had recently watched the Nova episode of Fabric of the Cosmos where they talk about spacetime as a sort of loaf where relative motion has the effect of cutting different angled slices out of the "loaf" of space time (for those who haven't seen the episode, it's basically textbook stuff on the relativity of simultaneity).

Anyway, that got me thinking about it. It's entirely possible for a distant observer moving towards me at great speed to observe that his "now-slice" contains things that from my perspective haven't happened yet, but these things will happen, does this imply some kind of determinism? I realize that there's no way for that distant observer to relay that information to me before it happens thanks to the limit of information being the speed of light I will always observe him observing my past, never my future.

It seems like I'm not the only person to have ever thought about this, I stumbled upon this when I searched for "Relativistic Determinism".

The more I think about it, maybe it's not that big of a deal (other than it being really weird), but is the logic sound? Is it possible for a distant observer to observe something that from my perspective hasn't happened yet? Or, in other words, is it valid to think of "all of time" existing in the same way we think "all of space" exists?

2. Feb 28, 2013

### Mentz114

This seems like a very dubious idea. Whether the event in question happened deterministically or not is not dependent in any way on whether one observer sees it before another. The event on your scenario happens, and therefore can in principle be observed at some time by all observers.

3. Feb 28, 2013

### RLutz

Maybe I'm not phrasing it correctly. I guess succinctly what I mean is, is it possible for some distant observer to see something in MY future (what shirt I'm going to wear tomorrow)?

And if it is possible for someone to see my tomorrow before it happens for me (even if there's no possible way they can convey that to me BEFORE it occurs for me), does that imply that future events in spacetime already exist?

4. Feb 28, 2013

### Staff: Mentor

No. As you point out, the distant observer can't relay any information to you faster than light; but not only that, the distant observer himself does not have the information about all the events in his "now slice" at the same time. At any given instant, he only has information about the events in his past light cone. He can *construct* a model of what is happening in his "now slice" based on that information, but it's only a construction. He doesn't actually have information (which must travel no faster than light) from events in his "now slice" that are distant from him.

5. Feb 28, 2013

### Staff: Mentor

Sure, he'll eventually see what you wear tomorrow. But he won't see it before you do, which is the point. Information can't travel faster than light; information from the event of you wearing something tomorrow will take time to travel to the distant observer. The fact that that event happens to be in the distant observer's "now slice" before then doesn't matter, because as I said in my last post, he can't receive information from all the events in his "now slice" at once.

6. Feb 28, 2013

### Mentz114

No. I think the answer above covers this. If any event is on my worldline, I know about it first - always. Any observer not co-located with me has a delay.

7. Feb 28, 2013

### RLutz

I follow what you guys are saying, and it makes perfect sense (if the information of what shirt I have isn't created till I wear it, then obviously no one can see that before me).

But what of the situation that I linked in the OP? http://www.kiekeben.com/relativistic.html

If I'm A, C is definitely in my future (hasn't occurred for me yet), but is in B's past (he already knows what's going to happen).

I think maybe I'm seeing what's going on here. It's not so much that B can tell what shirt I'm going to wear tomorrow, it's that he'll be able to see other events (a star exploding somewhere far away) before I am. That's less reality-shattering than him being able to tell which shirt I'm going to wear. Is this about right?

8. Feb 28, 2013

### Staff: Mentor

No, B does *not* know what's going to happen. That's the point. How can he know what happens at C, when light signals from C haven't reached him yet?

9. Feb 28, 2013

### 1977ub

http://en.wikipedia.org/wiki/Rietdijk–Putnam_argument

Increasingly these things strike me as a rebuttal of simultaneity itself. You can construct an inertial reference frame for an inertial observer. The next thing that happens is very often some type of misunderstanding! (e.g. twin paradox, ladder paradox, what have you).

10. Feb 28, 2013

### RLutz

11. Feb 28, 2013

### Staff: Mentor

Imagine a set of clocks that are synchronized in your rest frame of reference, and a second set of clocks that have been synchronized in the rest frame of reference of the distant observer (who is traveling relative to yourself at a high velocity). Imagine a second observer in his frame of reference who is, at present, directly opposite you. The distant observer will see a time on the clock directly opposite him within your frame of reference that is later than the time displayed on your clock as it is observed by the guy directly opposite you, assuming that both observers in the other frame are making their observations at the same time according to their own set of synchronized clocks. So, in this sense, the distant observer is seeing an event that is taking place (at a spatial location very far away) in what you would regard as your future.

12. Feb 28, 2013

### 1977ub

Nobody's seeing anybody's past [oops s/b "future"]. It's all a result of the confidence various observers have about what time on their own clock correlates with an event at some remote location. That process is not based on some simple observation but a framework of belief about what is simultaneous. In this respect, it's a bit like wondering if you're looking into the past if you can see someone across the international date line whose calendar reads what to you is yesterday's date.

Last edited: Feb 28, 2013
13. Feb 28, 2013

### Vorde

You can construct situations where an observer with non-zero velocity with regards to another observer such that they are at the same place at t=0 (so lorentz transformed from each other) such that one observer will 'see' an event happening at a $t=t_0$ that happens in the other reference frame at a time $t_1 > t_0$. But the key is that the math always works out such that the observer that sees the event at $t_0$ can never send a signal to the second observer before the second observer sees the event as well.

Saying it's determined isn't a good way of looking at it (GR is deterministic, as far as I know, but I don't think it's a good approach to this situation), rather I would say that it leads to the conclusion (which is completely equivalent to the relativity of simultaneity) that one observer will say they knew about the event before the other observer did.

14. Mar 1, 2013

### Fredrik

Staff Emeritus
The Andromeda argument* and similar ideas are in my opinion jumping to some rather silly conclusions for no good reason. Statements about what a person "sees" or "experiences", and about what events he "considers" simultaneous, are by definition statements about the coordinate 4-tuples assigned to events in spacetime by a coordinate system that we choose to associate with the observer's motion. It's not the structure of spacetime that determines if a classical theory is deterministic, and it's certainly not a convention for how to associate coordinate systems with moving observers. It's the equation of motion of the matter in the universe. If it has a unique solution for each initial condition, then the theory is deterministic.

Classical theories of matter in Minkowski spacetime (i.e. special relativity) are no more and no less deterministic than classical theories of matter in Galilean spacetime (i.e. pre-relativistic physics).

*) The version I read is this one. Search the page for "andromeda".

Last edited: Mar 1, 2013
15. Mar 1, 2013

### bobc2

Yes, you are not the only person. Google "Block Universe." Quite a few notable physicists have embraced this. Brian Greene's loaf of bread example is a good illustration of the concept. Block universe is a direct geometric picture of a universe populated by 4-dimensional objects as described by the mathematics of special relativity.

Some physicists feel that the block universe is a philosophical idea and should not be included with special relativity theory. Others reject the notion that block universe should be relegated to the philosophers and metaphysicists. Those opposing the philosophical basis feel that block universe is foundational to the math and physical understanding of the universe--having at least the position of a reasonable candidate for foundational studies in physics. Paul Davies identified it as one of the most profound problems for future generations of theoretical physicists.

Further, some feel there are other theories such as LET that are based on the same mathematics, leaving no preference for a 4-dimensional universe. However, given the contorted history of the development of LET into its present form, it is not clear that it really represents a theory separate from special relativity. The original motivation involving specific electromechanical effects producing physical shrinkage does not seem to have survived in the present LET. LET basically assumes Lorentz transformations and ether. A logical basis for the ether does not seem to be justified as part of LET nowadays, rather seeming to hang around as a historical artifact. Nevertheless, for some, LET is a logically viable alternative to special relativity and thus leaves the question open as to which theory is correct (notwithstanding those who hold that neither block universe nor ether have anything to do with the physics).

Wolfgang Rindler wrote in his text book that LET eventually disappeared into oblivion. I may not be attributing the following quote accurately, but I believe Lorentz (sometime after the dust had settled on LET vs. SR) said "...they can leave the question of the ether up to the metaphysicians."

This is not to push one theory or another but just to make you aware of some of the thinking on a very important subject that you bring up here.

It is no more weird than length contraction, time dilation or the twin paradox. And yes, the logic is sound. Block universe is entirely consistent with special relativity. To my knowledge no contradiction with special relativity has been found. Paul Davies claims that most physicists subcribe to it. These physicists feel it is not to be regarded as a separate theory, but rather an aspect of special relativity.

Einstein said that to a physicist there is no distinction between past, present and future.

Last edited: Mar 1, 2013
16. Mar 1, 2013

### Staff: Mentor

Well done, bobc2!

17. Mar 2, 2013

### someGorilla

No. Relativity of simultaneity per se does not imply any sort of determinism, or not for the reason you think. Newton's mechanics is already fully deterministic, Maxwell's electrodynamics is already fully deterministic, meaning that knowing the state of the universe *now* allows you to predict everything in the future. SR only gives new meanings to that "now" but doesn't change this. So you don't need relativity of simultaneity in order to have determinism.
In your example, your choice of shirt is in the other observer's past, but it's spacelike separated from him, that is it's not in his past light cone. He will only be able to see the colour of your shirt AFTER you have worn it - and THIS "after" is timelike so it's "after" for every observer. Actually, saying that your choice of shirt is in his past is only a matter of coordinate labelling, from the observer's point of view there is only what he knows (his past light cone) and the unknown (everything else). Your choice of shirt is in the everything else. It will eventually get into his past light cone, when he enters your future light cone, but that's way after you have worn your shirt!
However what you are describing is the concept of "block universe", which although metaphysical is, I think, espoused by a great many physicists. It's a coherent picture of spacetime, fully compatible with (though not implied by) SR. Whether it strikes you as deterministic depends on how undeterministic you viewed the universe yesterday :) Notice that nothing prevents you from seeing spacetime that way even in classical Newtonian dynamics.
Note that while you don't need any relativistic oddity in order to have determinism, on the other hand SR doesn't necessarily imply it: the standard model of particles is - well, depending on the interpretation - not deterministic, but it does include SR.

The Andromeda paradox is only a paradox in the etymological sense: something removed from common opinion. There is no contradiction whatsoever.
And the Rietdijk-Putnam argument is based on the vague meaning of the verb "exist" - I would expect more shrewdness from Putnam.

Also, I would like to suggest a different line of thought: SR defines simultaneity in a certain way. This is banally due to the fact that Lorentz transforms prove effective in going from one inertial frame to another without having to change the underlying laws. It's a nice mathematical tool that happens to work very well. But what does it mean PHYSICALLY that event A and event B are simultaneous according to observer X? NOTHING. This statement has no physical meaning. There is nothing in the events that makes them simultaneous. There is nothing in the structure of spacetime to make them simultaneous. There is even nothing that makes them "simultaneous for observer X". What matters is only how those events interact - and that is only at the new events where their light cones intersect. The arrangement of events on your grid of coordinates doesn't matter in the least. (And in GR this is most evident.) So whether you call them simultaneous or not, whether you define your changing clothes tomorrow as in the future or past of somebody else, it's just words. It's labels. Useful ones but labels.

18. Mar 2, 2013

### Staff: Mentor

I think that this is the key point. Relativity is compatible with both the deterministic classical mechanics and indeterministic quantum mechanics.